Question

[Nguyễn Trang Quyên]

tìm x, y thuộc Z cộng\(\frac{1}{x}+\frac{y}{2}=\frac{5}{8}\)

Answer 1

[conagninah]

X=8

Y=1

Answer 2

[Nguyễn Thị Thanh Tú]

\(\frac{1}{x}\)+\(\frac{y}{2}\)=\(\frac{5}{8}\)

=> \(\frac{5}{8}\)-\(\frac{y}{2}\)= \(\frac{1}{x}\)

=> \(\frac{5}{8}\)-\(\frac{4y}{8}\)=\(\frac{1}{x}\)

=>\(\frac{5-4y}{8}\)=\(\frac{1}{x}\)

=> (5-4y).x=1.8

=>(5-4y).x=8

=> 8 \(⋮\) (5-4y) , 8 \(⋮\)x

=> 5-4y \(\in\)Ư(8) , x\(\in\)Ư(8)

mà Ư(8)= { 1, -1, 2, -2, 4, -4, 8, -8 }

Ta có bảng

5-4y	1	-1	2	-2	4	-4	8	-8
x	8	-8	4	-4	2	-2	1	-1
y	1	\(\frac{3}{2}\)	\(\frac{3}{4}\)	\(\frac{7}{2}\)	\(\frac{1}{4}\)	\(\frac{9}{4}\)	- \(\frac{3}{4}\)	\(\frac{13}{4}\)

mà x,y \(\in\)z nên (x,y)=(8,1)

Vậy x=8, y=1